发表机构
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究非阿贝尔分数量子霍尔-超导体异质结构中的零模，提出将体威尔逊算符映射为局域零模算符的构造，并揭示不同拓扑序下的零模代数及隧穿特征，为探测Fibonacci缺陷结构提供普适签名。
AI 中文摘要
我们研究了由阿贝尔和非阿贝尔分数量子霍尔态构建的分数量子霍尔-超导体（FQH-SC）异质结构中束缚于电荷共轭缺陷的零模。尽管相关缺陷可由$G$-交叉辫张量范畴很好地描述，但其零模的局域算符描述通常未知。我们将局域零模算符的体-边界构造推广到具有非阿贝尔母拓扑序的FQH-SC，将折叠理论中的体威尔逊算符映射到一维FQH-SC理论中的局域零模算符。此构造区分了零模任意子与作用于缺陷希尔伯特空间的局域零模算符，并产生广义零模代数。它还确定了隧穿的融合道依赖性：零模算符的隧穿探测体单值性，而直接零模任意子转移探测$G$-交叉结合性数据。应用此框架，我们恢复了填充因子$\nu=1/m$的费米子Laughlin FQH-SC的$\mathbb{Z}_{2m}$ parafermion零模结构，获得了填充因子$\nu=1/m$的广义Moore-Read态的$\mathbb{Z}_2^{(n)}\times\mathbb{Z}_N$结构，其中费米子态$N=2m$，玻色子态$N=m$，并发现填充因子$\nu=3/(3M+2)$的$k=3$ Read-Rezayi态的$\mathrm{Fib}\times\mathbb{Z}_N$结构，其中费米子态$N=2(3M+2)$，玻色子态$N=(3M+2)/2$。在Read-Rezayi情形中，零模算符隧穿和直接零模任意子转移在中性融合道之间产生不同的普适振幅比，提供了底层Fibonacci缺陷结构的特征性签名。
英文摘要
We study zero modes bound to charge-conjugation defects in fractional quantum Hall-superconductor (FQH-SC) heterostructures built from Abelian and non-Abelian FQH states. Although the associated defects are well described by $G$-crossed braided tensor categories, a local operator description of their zero modes is not generally known. We generalize the bulk-to-boundary construction of localized zero mode operators to FQH-SCs with non-Abelian parent topological orders, mapping bulk Wilson operators in the folded theory to localized zero mode operators in the one-dimensional FQH-SC theory. This construction distinguishes zero mode anyons from the local zero mode operators that act on the defect Hilbert space and yields a generalized zero mode algebra. It also determines the fusion-channel dependence of tunneling: tunneling of zero mode operators probes bulk monodromy, while direct zero mode anyon transfer probes $G$-crossed associativity data. Applying this framework, we recover the $\mathbb{Z}_{2m}$ parafermion zero mode structure of fermionic Laughlin FQH-SCs at filling $ν=1/m$, obtain a $\mathbb{Z}_2^{(n)}\times\mathbb{Z}_N$ structure for generalized Moore-Read states at filling $ν=1/m$, with $N=2m$ for fermionic states and $N=m$ for bosonic states, and find a $\mathrm{Fib}\times\mathbb{Z}_N$ structure for the $k=3$ Read-Rezayi state at filling $ν=3/(3M+2)$, with $N=2(3M+2)$ for fermionic states and $N=(3M+2)/2$ for bosonic states. In the Read-Rezayi case, zero mode operator tunneling and direct zero mode anyon transfer yield distinct universal amplitude ratios between the neutral fusion channels, providing a characteristic signature of the underlying Fibonacci defect structure.
Comments63 pages, 5 figures
